The paper obtains a closed-form expression for the constrained Hodge dual of a p-form under the spherical constraint x_i x_i = 1, which reduces to the standard hypersurface Hodge star with unit normal.
On Pauli Reductions of Supergravities in Six and Five Dimensions
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
The dimensional reduction of a generic theory on a curved internal space such as a sphere does not admit a consistent truncation to a finite set of fields that includes the Yang-Mills gauge bosons of the isometry group. In rare cases, for example the $S^7$ reduction of eleven-dimensional supergravity, such a consistent "Pauli reduction" does exist. In this paper we study this existence question in two examples of $S^2$ reductions of supergravities. We do this by making use of a relation between certain $S^2$ reductions and group manifold $S^3=SU(2)$ reductions of a theory in one dimension higher. By this means we establish the non-existence of a consistent $S^2$ Pauli reduction of five-dimensional minimal supergravity. We also show that a previously-discovered consistent Pauli reduction of six-dimensional Salam-Sezgin supergravity can be elegantly understood via a group-manifold reduction from seven dimensions.
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Hodge Duals in Spherical Compactifications
The paper obtains a closed-form expression for the constrained Hodge dual of a p-form under the spherical constraint x_i x_i = 1, which reduces to the standard hypersurface Hodge star with unit normal.